The Inverse Hall-Petch Effect—Fact or Artifact?

2000 ◽  
Vol 634 ◽  
Author(s):  
Carl C. Koch ◽  
J. Narayan
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Computer Simulations ◽  
Nanocrystalline Materials ◽  
Grain Sizes ◽  
Average Grain Size

ABSTRACTThis paper critically reviews the data in the literature which gives softening—the inverse Hall-Petch effect—at the finest nanoscale grain sizes. The difficulties with obtaining artifactfree samples of nanocrystalline materials will be discussed along with the problems of measurement of the average grain size distribution. Computer simulations which predict the inverse Hall-Petch effect are also noted as well as the models which have been proposed for the effect. It is concluded that while only a few of the experiments which have reported the inverse Hall-Petch effect are free from obvious or possible artifacts, these few along with the predictions of computer simulations suggest it is real. However, it seems that it should only be observed for grain sizes less than about 10 nm.

Statistical analysis of the parameters and grain size distribution functions of single-phase polycrystalline materials

2020 ◽  
Vol 86 (4) ◽  
pp. 39-45
Author(s):  
S. I. Arkhangelskiy ◽  
D. M. Levin
Keyword(s):  
Grain Size ◽  
Distribution Function ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Single Phase ◽  
Distribution Functions ◽  
Grain Structure ◽  
Polycrystalline Materials ◽  
Grain Sizes ◽  
Average Grain Size

A statistical analysis of the grain size distribution is important both for developing theories of the grain growth and microstructure formation, and for describing the size dependences of various characteristics of the physical and mechanical properties of polycrystalline materials. The grain size distribution is also an important characteristic of the structure uniformity and, therefore, stability of the properties of the products during operation. Statistical Monte Carlo modeling of single-phase and equiaxed polycrystalline microstructures was carried out to determine the type of statistically valid distribution function and reliable estimates of the average grain size. Statistical parameters (mean values, variances, variation coefficient) and distribution functions of the characteristics of the grain microstructure were obtained. It is shown that the distribution function of the effective grain sizes for the studied polycrystal model is most adequately described by γ-distribution, which is recommended to be used in analysis of the experimental distribution functions of grain sizes of single-phase polycrystalline materials with equiaxed grains. The general average (mathematical expectation) of the effective grain size (projection diameter) with γ-distribution function (parameters of the distribution function are to be previously determined in analysis of the grain structure of polycrystalline materials) should be taken as a statistically valid and reliable estimate of the average grain size. The results of statistical modeling are proved by the experimental data of metallographic study of the microstructures of single-phase model and industrial materials with different degree of the grain structure heterogeneity.

Ultrasonic Discrimination of Samples With Differently-Distributed Grain Sizes and Equal Average Grain Size

1994 ◽  
Vol 362 ◽  
Author(s):  
Denise Nicoletti ◽  
Aran Anderson
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Theoretical Development ◽  
Volume Distribution ◽  
Size Estimation ◽  
Grain Sizes ◽  
Average Grain Size ◽  
Distribution Parameters ◽  
Ultrasonic Techniques

AbstractMaterials can have distributions of grain sizes. These distributions can have effects on the material's mechanical properties that are more complicated than an average grain-size dependence. The omission of distribution effects on properties is understandable in view of the great amount of labor required in the experimental measurement of grain volume distribution, together with the predominantly two-dimensional nature of micrography-based grain-size estimation. Ultrasonic techniques have been used to nondestructively measure the grain size of materials on a scale of microns. We suggest using ultrasonic attenuation as an alternative to micrography for three reasons. One advantage is that the ultrasonic dependence on size is a true, three-dimensional dependence. Secondly, through careful selection of wavelength, various grain-size distribution parameters can be extracted. The third justification is that ultrasonic techniques are quick and nondestructive. Previous theoretical development will be reviewed, and the experimental verification will be presented. Through numerical modeling we show the advantages of using ultrasonic techniques that are sensitive to grain-size distribution parameters. We demonstrate that samples with equal average grain size but different grain-size distributions have significantly different attenuation wavelength dependencies.

Recrystallization of Oxygen Contaminated Al Films

1986 ◽  
Vol 71 ◽  
Author(s):  
G.J. Van Der Kolk ◽  
M.J. Verkerk
Keyword(s):  
Grain Size ◽  
Silicon Nitride ◽  
Substrate Temperature ◽  
Oxygen Partial Pressure ◽  
Partial Pressure ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Relative Increase ◽  
Partial Pressures ◽  
Average Grain Size

AbstractAl was evaporated at oxygen partial pressures, PO2, varying between 10−7 and 10−4 Pa on substrates of silicon nitride. The substrate temperature was varied between 20 °C and 250°C. The films were annealed at temperatures up to 500°C.For Al films deposited at 20°C, it was found that the average grain size decreases with increasing oxygen partial pressure. After annealing recrystallization was observed. The relative increase of grain size was less for higher values of pO2. Annealing gave rise to a broad grain size distribution.For Al films deposited at 250°C, the presence of oxygen caused the growth of rough inhomogeneous films. This inhomogeneous structure remained during annealing.

Grain Size Distribution Effect on Mechanical Behavior of Nanocrystalline Materials

2004 ◽  
Vol 821 ◽  
Author(s):  
A.V. Sergueeva ◽  
N.A. Mara ◽  
A.K. Mukherjee
Keyword(s):  
Grain Size ◽  
Mechanical Behavior ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Nanocrystalline Materials ◽  
Tensile Deformation ◽  
Size Structure ◽  
Niti Alloy ◽  
Distribution Effect ◽  
The Matrix

AbstractGrain size distribution effect on the mechanical behavior of NiTi and Vitroperm alloys were investigated. Yielding at significantly lower stresses than found in equiaxed counterparts, along with well defined strain hardening was observed in these nanocrystalline materials with large grains embedded in the matrix during tensile deformation at temperatures of 0.4Tm. At higher temperature the effect of grain size distribution on yield stress was not revealed while plasticity was increased in 50% in NiTi alloy with bimodal grain size structure.

scholarly journals Modified Gompertz sigmoidal model removing fine-ending of grain-size distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Rui Yuan ◽  
Bo Yang ◽  
Yingfei Liu ◽  
Lingyu Huang
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Cumulative Probability ◽  
Second Stage ◽  
Grain Sizes ◽  
Third Stage ◽  
Moments Method ◽  
Sigmoidal Model ◽  
Parameters Calculation

Abstract Because of the laboratory operating, the fineending of grain-size distribution (GSD) are simply combined as one point, which results in the information loss of the fine and very-fine clastic particles, and affects the geological parameters calculation of GSD. To remove the fine-endings, a modified Gompertz sigmoidal model is proposed in this paper. The first stage is establishing and solving the modified Gompertz sigmoidal model; the second stage is fitting and evaluating the cumulative probability and frequency of GSD; the third stage is calculating the geological parameters. Taking 113 samples for example, coefficients of determination (COD) between measured and fitted individual cumulative probability and frequency are bigger than 0.98980 and 0.97000 respectively, which proves the goodness of fitting results. By moments method using frequency data, the COD between fitted and measured mean is 0.97578, while CODs of sorting, skewness and kurtosis are in low values, which suggest that the fine-endings has little influence on the average grain-sizes of GSD and large influence on its geometry. Besides, modified Gompertz sigmoidal model offers another quick numerical way to calculate median, mean and sorting of GSD by graphical method using cumulative probability data. The proposed method is useful to remove the fine-endings and contribute to calculate the geological parameters of GDS.

The Correlation Theory of 2D Normal Grain Growth

2004 ◽  
Vol 467-470 ◽  
pp. 1081-1086 ◽  
Author(s):  
M.W. Nordbakke ◽  
N. Ryum ◽  
Ola Hunderi
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Grain Size Distribution ◽  
Computer Simulations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Grain Structures ◽  
Spatial Grain ◽  
Kinetics Of

Computer simulations of 2D normal grain growth have shown that size correlations between adjacent grains exist in 2D grain structures. These correlations prevail during the coarsening process and influence on the kinetics of the process and on the grain size distribution. Hillert’s analysis starts with the assumption that all grains in the structure have the same environment. Since computer simulations contradict this assumption, the mean-field theory for normal grain growth needs to be modified. A first attempt was made by Hunderi and Ryum, who modified Hillert’s growth law to include the effect of spatial grain size correlations. In the 1D case the distributions derived by means of the modified growth law agreed well with simulation data. However, the distribution derived for 2D grain growth retained unwanted properties of the Hillert distribution. We review some recent progress in developing a mean-field statistical theory. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff.

Variable Elastic-Plastic Properties of the Grain Boundaries and Their Effect on the Macroscopic Flow Stress of Nano-Crystalline Metals

2009 ◽  
Vol 1224 ◽  
Author(s):  
Malgorzata Lewandowska ◽  
Romuald Dobosz ◽  
Krzysztof J Kurzydlowski
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Grain Boundaries ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Distribution Functions ◽  
Boundary Misorientation ◽  
Plastic Properties ◽  
Nano Crystalline ◽  
Average Grain Size

AbstractThe paper reports new experimental results describing properties and microstructure of nanocrystalline metals. Nano- and sub-micron aluminium has been produced by hydrostatic extrusion at ambient tempearture. The structures have been quantified in terms of size of grains and misorientation of the grain boundaries. Different average size of grains, variable normalized width of grain size distribution and changing grain boundary misorientation distribution functions have been revealed depending on processing parameters. The results of the tensile tests showed that the average grain size, grain size distribution and the distribution function of misorientation angles influence the flow stress of obtained nano-metals. In order to explain the observed difference in the properties of nano- and micro-sized aluminium alloys, a Finite Element Method models have been developed, which assumes that both grain boundaries and grain interiors may accommodated elastic and non-linear plastic deformation. These models assumed true geometry of grains (which differed in size and shape). Also, variable mechanical properties of grain boundaries have been taken into account (elastic modulus, yield strength and work hardening rate). The results of modelling explain in a semi-quantitative way macroscopic deformation of nano-crystalline aggregates. In particular, they illustrate the importance of the interplay between properties of grain boundaries and grain interiors in elastic and plastic regime.

Topology Based Growth Law and New Analytical Grain Size Distribution Function of 3D Grain Growth

2007 ◽  
Vol 558-559 ◽  
pp. 1183-1188 ◽  
Author(s):  
Peter Streitenberger ◽  
Dana Zöllner
Keyword(s):  
Grain Size ◽  
Distribution Function ◽  
Size Distribution ◽  
Grain Growth ◽  
Grain Size Distribution ◽  
Three Dimensional ◽  
Size Distribution Function ◽  
Change Rate ◽  
Grain Sizes ◽  
Self Similar

Based on topological considerations and results of Monte Carlo Potts model simulations of three-dimensional normal grain growth it is shown that, contrary to Hillert’s assumption, the average self-similar volume change rate is a non-linear function of the relative grain size, which in the range of observed grain sizes can be approximated by a quadratic polynomial. In particular, based on an adequate modification of the effective growth law, a new analytical grain size distribution function is derived, which yields an excellent representation of the simulated grain size distribution.

The Effect of Grain Size Distribution on the Mechanical Properties of Nanometals

2008 ◽  
Vol 140 ◽  
pp. 185-190 ◽  
Author(s):  
T.B. Tengen ◽  
Tomasz Wejrzanowski ◽  
R. Iwankiewicz ◽  
Krzysztof Jan Kurzydlowski
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Flow Stress ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Deformation Mechanisms ◽  
Average Grain Size ◽  
Significant Interest ◽  
Size Dispersion ◽  
The Relationship

Predicting the properties of a material from knowledge of the internal microstructures is attracting significant interest in the fields of materials design and engineering. The most commonly used expression, known as Hall-Petch Relationship (HPR), reports on the relationship between the flow stress and the average grain size. However, there is much evidence that other statistical information that the grain size distribution in materials may have significant impact on the mechanical properties. These could even be more pronounced in the case of grains of the nanometer size, where the HPR is no longer valid and the Reverse-HPR is more applicable. This paper proposes a statistical model for the relationship between flow stress and grain size distribution. The model considered different deformation mechanisms and was used to predict mechanical properties of aluminium and copper. The results obtained with the model shows that the dispersion of grain size distribution plays an important role in the design of desirable mechanical properties. In particular, it was found that that the dependence of a material’s mechanical properties on grain size dispersion also follows the HPR to Inverse-HPR type of behaviour. The results also show that copper is more sensitive to changes in grain size distribution than aluminium.

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